$f(x) = x^{2}+5x+3$ $h(t) = -4t-3(f(t))$ $g(t) = 3t+5(f(t))$ $ f(h(-4)) = {?} $
Answer: First, let's solve for the value of the inner function, $h(-4)$ . Then we'll know what to plug into the outer function. $h(-4) = (-4)(-4)-3(f(-4))$ To solve for the value of $h$ , we need to solve for the value of $f(-4)$ $f(-4) = (-4)^{2}+(5)(-4)+3$ $f(-4) = -1$ That means $h(-4) = (-4)(-4)+(-3)(-1)$ $h(-4) = 19$ Now we know that $h(-4) = 19$ . Let's solve for $f(h(-4))$ , which is $f(19)$ $f(19) = 19^{2}+(5)(19)+3$ $f(19) = 459$